A diffusive predator-prey system with prey refuge and predator cannibalism

1.   Introduction

Even though the detrimental effects of COVID-19 have not been wiped away, the recent energy crisis is rumbling for another global crisis. Inflation is at record highs, tangling financial markets, energy price uncertainty, and alternative investments all motivate us to conduct this study, which is encapsulated with three timely objectives: Testing the dynamic return and volatility coherence among cryptocurrency, volatility index, and commodities with stock markets. Then, we investigate the volatility spillover among stock markets and other variables. Finally, we try to know the hedge and safe haven assets for emerging and developed stock market investors.

1.1.   Hedge

A hedge or safe haven typically exhibits zero or negative correlation, in contrast to a diversifier, which may demonstrate a positive but imperfect correlation with other assets or a portfolio (Baur and McDermott, 2010) and Lucey, 2010). The former has a negative or zero correlation with other portfolio assets, whereas the latter is anticipated to display similar negative or zero correlation traits during a crisis period. A robust hedge exhibits a negative correlation, whereas a weak hedge demonstrates no correlation with other assets or a portfolio (Baur and McDermott, 2010). The robustness of a safe haven can be similarly perceived, especially in times of crisis. The nuanced distinction between a hedge and a safe haven can be seen as follows: A hedge is effective in all situations, whereas a safe haven is mostly utilized during periods of crisis.

1.2.   Gold as Hedge

Historically, conventional assets like gold serve as a primary buffer against price volatility in other assets (Shiva and Sethi, 2015). Precious metals such as gold, silver, and platinum demonstrate hedging potential, particularly during periods of significant stock market volatility (Hillier et al., 2006; Uddin et al., 2020). Gold is universally acknowledged as a long-standing safe haven, in order to provide hedging strategies on the financial risks involved in such crises, and considering that two cryptocurrency prices have been impacted by Russia-Ukraine war uncertainties apart from the COVID-19 pandemic, we apply wavelet analysis along with multivariate DCC-GARCH process to scrutinize return–volatility causal relationship among gold price and six stock market indices, including three well-established emerging economies (EEs). We achieve a more balanced and complete picture by considering data for the time period July 28, 2016 to December 30, 2022. The events of analysis are crises in the Chinese market, a trade war between the USA and China, caused by the COVID-19 pandemic, after which will come global recession Ⅲ (a Russia-Ukraine war); next, part Ⅳ — the peak of the global energy crisis. The findings generally indicate that when a sudden shock like this happens (or in a pandemic), there is no one other than Ethereum for all investors in emerging and developed markets to find a safe haven or protect themselves, while Bitcoin acts as less safe. We also show Gold as a hedge in Global Crises and as a Hedge and Weak Safe Haven Against Geopolitical Tension. Last, investors in the paired joint oil stock have a greater benefit but can only gain if they hold shorter-term investments. As for volatility, arguably, only bitcoin is observed as the least volatile among all other variables. Our findings suggest stock markets are the source of volatility spillover to all others, while prior work has established mixed evidence during the pandemic, the most crucial and recent periods, respectively (Agyei-Ampomah et al., 2014; Gürgün and Ünalmış, 2014; Miyazaki and Hamori, 2016), possessing the capacity to mitigate inflationary risk (Blose, 2010; Beckmann and Czudaj, 2013; Balcilar et al., 2017b; Valadkhani et al., 2022).

In an early study investigating the hedging and safe haven attributes of gold relative to the stock and bond markets in Germany, the UK, and the US, gold is identified as a hedge for equities and a safe haven during periods of market distress (Baur and Lucey, 2010). Multi-economy research indicates that gold serves as both a hedge and a robust safe haven for developed markets but is not essential for rising economies like the BRIC nations (Baur and McDermott, 2010).

Conflicting results are also documented (Ghazali et al., 2013). Gold serves as both a hedge and a diversifier, albeit its effectiveness is contingent upon certain markets (Beckmann et al., 2015). Specifically, gold has not been observed to function as a hedge or a safe haven for Thai investors (Gürgün and Ünalmış, 2014; Wen and Cheng, 2018). The hedging efficacy of gold against oil risk is also unsubstantiated (Ciner et al., 2013; Salisu and Adediran, 2020; Liu and Lee, 2022).

1.3.   Cryptocurrency as hedge

Developments in e-commerce and the emergence of virtual currencies, such as Bitcoin and Ethereum, have established new domains in investment behavior. Following its introduction after the Global Financial Crisis, Bitcoin has significantly altered financial practices related to the issuance, storage, and transfer of money. It has been characterized as either a speculative asset (Baek and Elbeck, 2015) or a digital equivalent of gold (Popper, 2015; Baur and Hoang, 2021; Selmi et al., 2022).

Bitcoin has emerged as a significant alternative to gold regarding safe haven properties, despite ongoing controversies and challenges related to policy, economic factors, and user concerns, particularly regarding its volatility (Brandvold et al., 2015; Cheah and Fry, 2015; Dwyer, 2015; Katsiampa, 2017; Balcilar et al., 2017a; Chaim and Laurini, 2018; Gandal et al., 2018). This results from its distinctive characteristics, including independence from third-party manipulation, serving as a medium of exchange, facilitating transactions, and lowering transaction costs, alongside the enthusiasm among its users (Kim, 2017; Gajardo et al., 2018; Erdin et al., 2020).

Bitcoin, as a prominent cryptocurrency, increasingly attracts investor attention as a hedging instrument (Urquhart and Zhang, 2019; Kang et al., 2020; Chkili et al., 2021). It serves to diversify risks related to various factors, including exchange rates (Dyhrberg, 2016b; Wang et al., 2016b), inflation (Blau et al., 2021; Conlon et al., 2021), the money market (Sauer, 2016), and energy commodities (Bouri et al., 2017b; Rehman and Kang, 2021).

Examining the hedging properties of Bitcoin in relation to currencies reveals that Bitcoin serves as a hedge for some currencies while acting as a diversifier for others (Urquhart and Zhang, 2019). Comparable findings are observed regarding the hedging effectiveness of gold and Bitcoin in relation to oil price fluctuations (Selmi et al., 2018; Salisu et al., 2023). Furthermore, substantial evidence supports the assertion that Bitcoin serves as an effective hedge against global uncertainty (Bouri et al., 2017a; Wu et al., 2019; Al-Nassar et al., 2023).

Similar results are observed regarding the hedging of stock indices, such as the FTSE 100 index (Dyhrberg, 2016a). Evidence from the GARCH model indicates that Bitcoin serves as a robust hedge against the Euro STOXX, Nikkei, Shanghai A-Share, S&P 500, and TSX index (Chan et al., 2019).

Additionally, research indicates that the hedging characteristics of Bitcoin warrant further investigation. The BEKK-GARCH model indicates that the hedging capacity of Bitcoin relative to gold fluctuates based on portfolio composition and temporal factors (Klein et al., 2018). Bitcoin is regarded as an immature market and is not advised as an investment vehicle for downside protection (Smales, 2019). Concerns regarding the effectiveness of Bitcoin as a hedge, than as a diversifier, have been noted (Bouri et al., 2017a; Charfeddine et al., 2020).

1.4.   Crises

The COVID-19 pandemic has been identified as a direct or indirect cause of investor apprehension in global financial markets from its onset (Sun et al., 2020; Ji et al., 2020; Salisu et al., 2021). During the pandemic, gold does not exhibit its safe-haven characteristics (Cheema et al., 2022). Therefore, it is prudent to further investigate the implications beyond the conventional capacities related to digital currency (Alfaro et al., 2020; Corbet et al., 2021), particularly with diversification and volatility (Platanakis and Urquhart, 2020; Shen et al., 2020).

During this unprecedented era marked by the COVID-19 pandemic, the Russia-Ukraine conflict, the global energy crisis, the Chinese market turmoil, and the US-China trade war, it is imperative and valuable to examine the hedging capabilities of gold and cryptocurrencies against both emerging and developed market indices amidst these crises, a topic that remains underexplored in the literature. In this study, we enhance the literature by examining the hedging capacity of cryptocurrencies, particularly in the context of crisis risks for stock markets, in comparison to gold, crude oil, and the cryptocurrency volatility index, despite extensive prior research on the relationship between cryptocurrencies, especially Bitcoin, and gold (Baur et al., 2018; Bouoiyour et al., 2019; Wu et al., 2019; Jareño et al., 2020; Naeem et al., 2020; Shahzad et al., 2020). Most research on cryptocurrency hedging literature has focused on Bitcoin and established stock markets (Bouri et al., 2020; Baur et al., 2022; Cai et al., 2022; Yousaf et al., 2023), but this study broadens the traditional cryptocurrency selection to include both Bitcoin and Ethereum. Prior research on Bitcoin and Ethereum underscores the preeminence of Ethereum as a more advantageous choice in the cryptocurrency sector (Beneki et al., 2019; Mariana et al., 2021; Kassamany et al., 2022). With the onset of the Russian invasion, global tensions and energy prices are escalating, both of which are critical for economic activity, while financial markets are declining and inflation is increasing.

With these discussed, our contribution to financial literature is threefold. First, given the dominance of Bitcoin among alternative investments (Shahzad et al., 2020; Shahzad et al., 2022), even though a vast number of studies present in this domain, it is unclear for most cases in terms of Ethereum: The second largest cryptocurrency with market capitalization and dominance as whether cryptocurrencies are hedge for stock markets and are similitude to gold or other uncertainty indices. To the best of our knowledge, acknowledging the versicolor findings on the interaction between Bitcoin and Ethereum, we add to the cryptocurrency and financial hedging literature by drawing a comparison of both the cryptocurrencies with stock markets from both emerging and developed nations.

In addition to that, we employ a new uncertainty index (Cryptocurrency Volatility Index, CVI) which is yet to be analyzed. Similar to the stock market's implied volatility, VIX, CVI depicts the 30-days future expected volatility in the overall cryptocurrency market (Nguyen et al., 2022). Given the growing political and regional uncertainties amidst the Russian invasion, thus understanding the dynamics of these cryptocurrencies alongside commodities and volatility index against a wide range of stock markets will aid investors and fund managers in designing an appropriate profitable investment plan.

Finally, designing a profitable investment plan requires an understanding of movements and co-movements at various points in time and investment horizons. In this context, our methodological approach fits best (Sifat et al., 2019; Celeste et al., 2020) as it identifies investment possibilities decomposed in time and frequency, which are invaluable for investors, fund managers, and policymakers. we also study the volatility spillover among cryptocurrency and other indices through phase difference (Kumar and Anandarao, 2019), which is also a valuable addition to the cryptocurrency and financial market contagion literature considering the current turmoil in the financial markets.

From our return analysis findings, Ethereum's capability in acting as safe haven for investors from both emerging and developed markets at time of sudden shock (or pandemic) while Bitcoin offers limited safeguarding. Additionally, high the co-movement among cryptocurrency and stock markets are observed during heightened geopolitical tensions. We also show gold as a hedge during global crises while a hedge and weak safe haven against geopolitical tension. Finally, investors with joint oil-stock pairs may only benefit from shorter investments.

With respect to volatility, arguably, we found only bitcoin as the least volatile among all other variables observed. We show stock markets are the net emitters of volatility spillover toward others, where during the pandemic, we observed most spillover evidence and considerably negligible evidence persisted during the recent period. These findings are anticipated to enable potential investors to more effectively select their investment kinds and create their investment portfolios while providing significant insights for policymakers.

Here, we utilize wavelet and multivariate GARCH methods to analyze the relationship between gold, two cryptocurrencies, and six typical market indices: Nifty 50, FTSEIndo (FTSE Indonesia), Nikkei 225, FTSEMY (FTSE Bursa Malaysia KLCI), FTSE 100, and S&P 500. The continuous wavelet transform (CWT) has emerged as a significant tool for analyzing time-varying and time-scale dependent market return co-movements within time series, as evidenced by various studies in economics and finance (Bhuiyan et al., 2021; Bouri et al., 2020; Cai et al., 2022; Kumar and Padakandla, 2022). While most conventional econometric techniques cannot be applied directly, the wavelet method effectively addresses stylized facts such as nonstationarity or nonlinear lead-lag interactions frequently observed in financial time series, partly due to the heterogeneous expectations and risk perceptions of investors across investment horizons.

In Section 2, we delineate the Continuous Wavelet Transform (CWT) and multivariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. In Section 3, we present the data utilized to assess the correlation and the corresponding outcomes. In Section 4, we conclude the analysis by outlining potential future directions.

2.   Methodology

We apply CWT, to convert the time series, a function of a single variable, namely, time, into a function encompassing two distinct variables: Time and frequency. Upon representing the series correlations in a two-dimensional format, it becomes feasible to discern and interpret underlying patterns or concealed information. This analytical process, known as wavelet coherence, serves to quantify the extent of association among the variables across varying time and frequency intervals.

We use the multivariate DCC-GARCH approach to evaluate a portfolio's dynamic conditional correlation (DCC). In particular, we use the DCC model with a multivariate t-distribution to account for the fat-tailed nature of asset returns, gauge the risk associated with the tail aspects of returns, and pinpoint the benefits of diversification.

2.1.   Continuous Wavelet Transform

In this analysis, we select a wavelet filter. Based on the literature, a moderate filter length is required to capture the specifications and features of time series data (Gallegati, 2008). We implement an LA (8) filter since this filter is the least asymmetric wavelet filter and concedes smoother wavelet coefficients compared to the Haar wavelet filter. Besides, the LA (8) filter with a length of L = 8 based on eight nonzero coefficients (Antonini et al., 1992) confirms stability among sample size and filter length (An et. al., 2013).

The continuous wavelet transform, ${W}_{x}\left(s, \tau \right)$, is produced by performing a projection of a mother wavelet $\psi$ onto the time series being investigated $x\left(t\right)$ $\in {L}^{2}\left(R\right)$,

That is,

The wavelet's positions in the time and frequency domains are denoted by τ and s, respectively. The wavelet transform provides simultaneous information on time and frequency by representing the original series as a function of τ and s. Wavelet coherence is utilized to explore the interaction between two time series and the degree to which a linear transformation integrates them.

where S is a smoothing operator, s is a wavelet scale, ${W}_{x}\left(s, \tau \right)$ is the wavelet transform of the x, ${W}_{y}\left(s, \tau \right)$ is that of y, and ${W}_{xy}\left(s, \tau \right) = {W}_{x}\left(s, \tau \right){W}_{y}^{*}\left(s, \tau \right)$ is the cross wavelet transform of the two time series (Aguiar-Conraria and Soares, 2011, Vacha and Barunik, 2012).

The wavelet squared coherence ${R}^{2}\left(s, \tau \right),$ which is measured on a scale from 0 to 1, quantifies the degree of association between variables x and y. A value approaching zero indicates a weak correlation, whereas a value approaching one signifies a strong correlation.

2.2.   Multivariate GARCH

The estimation of the DCC method comprises two sequential steps while employing the multivariate GARCH model. The univariate volatility parameters are initially assessed for each variable, resulting in the estimation of two GARCH equations for two variables. For instance, the asymmetric GARCH equation (Glosten et al., 1993) is a pertinent example.

where I represent an indicator function that equals 1 when the standardized residual of the series $\varepsilon = \left\{{\varepsilon }_{t}\right\}$ is positive and 0 otherwise. A negative value of ${c}_{2}$ indicates that periods of higher variances promptly succeed periods of negative residuals compared to those of positive residuals. The GARCH equation is utilized to estimate the residual for each variable.

Deriving the parameters of the DCC equation, a time-varying correlation matrix can be computed using the residuals from the initial stage as inputs.

where ${H}_{t}$ measures the conditional covariance matrix, ${D}_{t}$ denotes the diagonal matrix, which contains the conditional time-varying standardized residuals. This residual is obtained from the univariate GARCH model as the on-diagonal elements or variances. The off-diagonal elements denoted as Rt indicate the time-varying correlation matrix (Engle, 2002, Tse and Tsui, 2002).

Therefore, the likelihood of the DCC estimator is:

Initially, we maximized the volatility component. This indicates that the log-likelihood is reduced to the sum of the univariate GARCH equations. Conditional on the estimated ${D}_{t}$, with the standardized residual series computed in the first step, the correlation component ${R}_{t}$ is maximized in the next step. In the third step, the nonnegative parameters $\alpha and\beta$ those satisfy $\alpha +\beta \le 1$ are estimated using the following DCC equation (6).

When the value of $\beta$ approaches 1, it indicates a substantial degree of persistence in the series for correlation ${R}_{t}.$ If the value of $\alpha +\beta$ approaches 1, signifies high persistence in the conditional variance. The model demonstrates GARCH-type dynamics for both conditional correlation and variance. The time-varying conditional variance serves as a measure of uncertainty, offering valuable insights into the drivers of variance movements.

3.   Results

We aim to examine the interrelationships among various asset classes using wavelet coherence analysis in MATLAB and R Studio. The data utilized for the study will be detailed in Section 3.1, with the subsequent findings presented in Section 3.2.

3.1.   Data

The data extracted from DataStream spans from 28th July 2016 to 30th December 2022, encompassing key events such as the Chinese market crisis, the US-China trade war, the COVID-19 pandemic, and the Russia-Ukraine war. It includes six representative indices from both emerging and developed economies: Nifty 50, FTSEIndo for FTSE Indonesia, Nikkei 225, FTSEMY for FTSE Bursa Malaysia KLCI, FTSE 100, and S&P 500. These indices and gold and cryptocurrency prices are transformed into market returns using natural logarithmic differences.

India's primary National Stock Exchange index (NSE) is the NIFTY 50. It is calculated using a process that takes market capitalization into account and adjusts for float. The index follows the performance of a portfolio of blue-chip firms, which are the biggest and most liquid Indian stocks that are listed on the NSE and have their headquarters in India. A price-weighted average of 225 highly regarded Japanese companies listed in the first sector of the Tokyo Stock Exchange is known as the Nikkei 225 stock average. Furthermore, the top 30 businesses on the Bursa Malaysia main board by total market capitalization are included in the FTSE Bursa Malaysia KLCI index. A capitalization-weighted index of the top 100 highly capitalized companies trading on the London Stock Exchange is called the Financial Times Stock Exchange 100 Index.

Moreover, the S&P 500 is a stock market index that assesses the stock performance of 500 large companies listed on stock exchanges in the United States. It is widely recognized as the foremost measure of large-cap U.S. equities. The corresponding tickers for the data are detailed in Table 1.

Table 1.  Specification of data.

Index	Ticker
Gold Spot Price	GOLD
Bitcoin Price	BTC
Ethereum Price	ETH
Cryptocurrency Volatility Index	CVI
West Texas Intermediate	WTI
NSE Nifty 50	NIFTY
FTSE Indonesia	FTSEINDO
Nikkei 225	NIKKEI
FTSE Bursa Malaysia KLCI	FTSEMY
Financial Times Stock Exchange 100 Index	FTSE 100
Standard & Poor's 500	S&P 500

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3.2.   Findings

The findings are presented in this section, including the dynamic conditional correlation in Section 3.2.1, the wavelet coherence in Section 3.2.2, the volatility connectedness in Section 3.2.3, and the volatility spillover in Section 3.2.4.

3.2.1.   Dynamic Conditional correlation (DCC)

Regarding dynamic connectedness among cryptocurrencies, the cryptocurrency risk index, gold, and WTI indices with respect to stock indices from emerging and developed economies, Figure 1 shows the DCC-MGARCH outputs, with the model fit outcomes being provided in Appendix 1.

Figure 1.  Dynamic Conditional Correlation among indices.

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Considering the dynamic correlation between cryptocurrencies and stock indices, it was found that Nikkei and FTSE Indonesia have the highest and lowest conditional correlations, respectively, for both cryptocurrencies. Interestingly, a consistent margin is observed among the connectedness of all indices; for instance, an increase in correlation of one index increases correlation for others as well. Surprisingly, even though Bitcoin held a relatively weaker conditional correlation with stock indices prior to the pandemic, which saw substantial increments during the pandemic, but following the start of the Russian-Ukraine war, a jump in conditional correlation is noticed among pairs with Ethereum, which at some point clocked to nearly +1.20 (for ETH-Nikkei). Even though an irregular conditional correlation is observed between Bitcoin and the stock indices for the pre-pandemic period, the opposite is seen for Ethereum. That is, for Ethereum, from the start of 2017, we observe a downward slope in the correlation graph, which turned otherwise following the start of Covid-19 and magnified significantly from 2022.

Few possible interpretations for this jump could be drawn from previous studies where, compared with Ethereum, Bitcoin was found relatively more sensitive to extreme downward movements in oil than upwards, while Ethereum was more sensitive to upward shocks than downwards (Conlon et al., 2024, Kassamany et al., 2022, Li et al., 2022). Moreover, the reaction of both cryptocurrencies varies with market movements and global conditions, where Bitcoin's reaction is significantly higher than Ethereum (Mariana et al., 2021, Marobhe, 2022, Raheem, 2021) while Ethereum's reaction is larger than Bitcoin's with presence of geopolitical or economic policy uncertainty (Będowska-Sójka et al., 2022, Theiri et al., 2023).

Gold and WTI graphs can be termed as retrogressive. From the start and until the end of the sample period, we observe a series of inverse relationships among both indices while correlating with stock indices. As such, we saw, until 2018, that gold had a negative correlation with most stock indices, where −0.60 with Nikkei was recorded as the highest while WTI had the highest (positive) correlation with all indices. A falling slope is noted, which strengthened again in the following periods until Covid-19 came in when the connectedness weakened but did not turn negative in the early periods. The negative connectedness is visible for pairs with gold from late 2018 when several events took place concerning financial hubs like the Wallstreet, for instance, tension with the China-US trade war (Christou et al., 2021, Qiu et al., 2019, Shi et al., 2021), interest rate uncertainty (Moussa et al., 2021, Wang et al., 2019), regulatory pressures on tech industry (Liu et al., 2022, Metz et al., 2020) etc. Then came the global pandemic and the correlation is visible significantly low where stock markets plummeted fearing risk and uncertainties while pushing investors towards gold leading price to soar (Drake, 2022, Hung and Vo, 2021, Mensi et al., 2022). With the vaccine announcement, the increased fear starts to evaporate, and markets start to regain stability where we observe increasing positive connectedness among gold and stock indices as well as with WTI index.

Similarly, with the start of the Russian-Ukraine war where oil was used as a valuable weapon (through supply cuts leading price to soar and resulting in global uncertainty again), a significant negative connectedness is observed among gold, WTI, and stock indices. However, with time, the effect soon started to fade away, turning to a positive connectedness among the indices.

Not to mention, crypto volatility has always been coupled with cryptocurrency discussions since their introduction. This includes cryptocurrency and mainstream ones, where Bitcoin and Ethereum, in particular, have been widely studied in the literature, thus claiming their high volatilities with respect to other financial instruments such as stocks. Our dynamic correlation here provides no unusual facts in relation to the cryptocurrency volatility index (CVI) and stock indices from both emerging and developed nations. We observe a constant negative correlation among the pairs, which turned positive but short-lived in April 2021 and the last quarter of the same year. The positivity in the first and final quarters of 2021 is notable for the developed nations and not for the emerging ones, and government support packages could be one of the possible reasons (Beer et al., 2023, Macartney et al., 2022) as the developed nations' governments have more to support their people compared to the emerging nations'. Similarly, with the start of the war in 2022, the connectedness among pairs start to drop and turn significant as developed nations were more responsive with Nikkei and S&P 500 as the leading ones, respectively.

3.2.2.   Return series (wavelet)

Upon understanding the dynamic correlation pattern, we further conducted wavelet coherence analysis to validate the DCC findings and to have a better understanding of investment horizons. The results of the wavelet coherence are presented in Figures 2–6.

Figure 2.  Wavelet coherence between Bitcoin and stock markets.

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Figure 3.  Wavelet coherence between Ethereum and stock markets.

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Figure 4.  Wavelet coherence between cryptocurrency volatility index and stock markets.

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Figure 5.  Wavelet coherence between gold and stock markets.

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Figure 6.  Wavelet coherence between oil and stock markets.

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Upon investigating cryptocurrency and stock markets from emerging and developed nations, the wavelet coherence analysis shows, on average, that cryptocurrencies are relatively isolated from the conventional financial markets given the absence of major global turmoil such as the COVID-19 pandemic. Our results in Figures 2 and 3 show the dominance of blue regions over warmer colors in pre-pandemic periods, with some minor exceptions during 2018, which are linked to the US-China trade war and the great cryptocurrency crash. Moreover, even though relatively higher cooler zones in relation to Bitcoin's pairwise connectedness prior to 2020, we note a significant transition to warmer regions following 2020 indicating growing integration among mainstream cryptocurrency and conventional financial markets. Additionally, Bitcoin's maturity may also play a role in strengthening this connectedness.

With respect to investment horizons and decisions, our results indicate a high-order connectedness among Bitcoin and other indices over medium- and long-term investment horizons, which significantly shrinks for Ethereum over longer horizons only. Even though both cryptocurrencies hold notably high connectedness in medium horizons, for shorter horizons, both maintain a low form of correlation.

Finally, our causal investigation findings are more interesting. Given the similar market structures among Bitcoin and Ethereum, we observe their heterogeneous behavior against stock indices. For instance, prior to the cryptocurrency crash and the US-China trade war, Bitcoin had positive connectedness with S&P500 and Nikkei 225 and Ethereum was negative over shorter horizons. Similarly, despite having positive connectedness over medium and longer horizons among both cryptocurrencies and other indices during the early Covid period, considering shorter horizons, Bitcoin was positively connected while Ethereum was negatively connected. Last, considering the recent periods (starting 2022), we note both cryptocurrencies are perfectly positively correlated with stock indices over all horizons, except Ethereum being perfectly negatively correlated with S&P 500 over the shortest horizon (2–4 days). Finally, with respect to causal impact, considering the pre-Russian-Ukraine war, we found, in most cases, that Bitcoin leads other indices while Ethereum lags; the only exception is against S&P 500, where both cryptocurrencies lag.

Our analysis then proceeds with investigating connectedness among Cryptocurrency risk index and stock indices. Analyzing all the pairs in Figure 4, we summarize our findings through a negative linkage between the risk index and stock indices. In particular, at times of global tensions such as the Covid pandemic and the ongoing Russian-Ukraine war, we found significant negative coherence over medium investment horizons among all the pairs assessed. The strong coherence faded with the fading of the pandemic, which again rebounded through the Russian-Ukraine war in early 2022 but with a moderate degree, which was limited to a medium range of investment horizon only. However, in both instances, we note stock indices causing this coherence, indicating the muted ability of the cryptocurrency risk index to act as a signaling agent to safeguard stock market investors.

Our observation from Figure 5 criticizes the safe haven labeling of gold to some extent. Empirical findings advocating gold as safe haven (Baur and Lucey, 2010, Baur and McDermott, 2016, Reboredo, 2013b); however, while looking at our wavelet coherence observations over the global pandemic period ranging between early 2020 until late 2021, we note a positive connection among gold and stock indices where, for all medium investment horizons, stock indices are leading while, for longer versions, gold is leading, which contradicts most literature relating to Covid-19 in general (Long et al., 2021, Salisu et al., 2021, Triki and Maatoug, 2021) and stock markets in particular (Hasan et al., 2021, Huang and Chang, 2021, Shahzad et al., 2020). Moreover, for shorter horizons, we also find inconsistencies. For instance, a positive correlation is noted for FTSE Indonesia and FTSE 100, while the rest maintained a negative correlation. Surprisingly, with the rise of new global fear as a consequence of the Russia-Ukraine war, unlike others, we observe relatively low coherence and evidence of some negative connectedness among gold and stock markets and, in most occasions, gold is leading, making them ideal for both diversifying and hedging geopolitical tension reiterating with previous events (Baur and Smales, 2020, Tiwari et al., 2020).

The oil-stock nexus has always been an interesting topic of discovery due to its connectedness through the macroeconomic channel and is widely reflected through scholarly literature. Our dynamic results in Figure 6 show extreme coherence effects. We note, for all indices, the highest level of coherence (perfectly correlated: correlation +1) over longer versions, consistently. In fact, we also observe prolonged periods of high coherency only in the case of FTSE Malaysia, which extends until the end of the sample period. One possible reason for this extension may relate to Malaysia's standing as an oil producer while the other economies are oil consumers. As such, based on this, we argue on the notion that the coherence or dependence among oil and stock markets may also be defined through an economy's standing on oil (i.e., as producer or consumer). That is, the effect of oil price shock will be reflected over long-term investment horizons in stock markets for oil-producing nations at a relatively higher magnitude than oil-consuming nations, which is consistent with (Ashfaq et al., 2019, Rizvi and Masih, 2014). Further, even though stock indices are leading on average, evidence of the opposite is also present. For instance, with respect to NIFTY and FTSE 100, we see WTI returns are leading for the longest horizons (128 days and beyond), and for others, we found that stock indices are leading. While mild coherency is observed for medium horizons only during Covid periods and was not prolonged, but for short-term investors, no major impact has been noticed.

Therefore, we conclude our return coherence analysis among cryptocurrency, cryptocurrency risk index, gold, and oil index with stock indices from emerging and developed nations first, based on cryptocurrency's pairwise coherence analysis, and we argue Ethereum's capability in acting as a safe haven for investors from both emerging and developed markets at a time of sudden shock (or pandemic) while Bitcoin offers limited safeguarding (only for FTSE Indonesia over the shortest horizon), reiterating (Mariana et al., 2021). In addition to this, with the presence of an augmented global geopolitical and economic tension through the Russian-Ukraine war, the cryptocurrencies and other stock indices experiencing substantial volatilities partially support (Khalfaoui et al., 2022, Umar et al., 2022); thus, our results show evidence of perfect positive correlations over various horizons for different indices whereby mostly cryptocurrencies are leading. Even though Ethereum's correlation with others is distinctive in magnitude compared with Bitcoin over longer horizons, it may act as a diversifier, and we note dimmed investment opportunities (beneficial) by holding both (cryptocurrency and stock) at the same time.

For gold, we conclude that a high coherence leading through stock indices is observed for long-term investors at the time of the covid pandemic, compromising the conventional safe haven feature of gold. However, for short- and medium-term investors, we found evidence advocating gold as a valuable diversifier and hedge for stock indices. Moreover, concerning the recent uncertainties led by the Russian-Ukraine war, our coherence analysis reveals evidence of gold acting as a strong hedge and a weak safe haven for all stock indices, but no evidence of their strong and safe haven has been noted. Thus, we argue gold as a hedge during a global crisis while a hedge and weak safe haven against geopolitical tension, which is in line with recent findings by (Selmi et al., 2022).

Reflecting on oil, an ascending order of connectedness was revealed among investment horizons and levels of coherence. That is, the highest degree of connectedness was evident over long-term horizons throughout the pandemic period for all indices, which slightly reduces for medium horizons while almost vanishing for shorter horizons. Additionally, oil dependence plays a significant role in explaining the oil-stock nexus. With the absence of global events such as the Covid pandemic, an oil-producing nation's stock index tends to hold higher connectedness whereas an oil-consuming nation's indices tend to hold relatively weaker.

3.2.3.   Volatility connectedness

Prior to testing for volatility spillover, similar to return connectedness, we first try to understand the volatility connectedness among indices. The volatility connectedness in Figure 7 shows contradicting outcomes when compared with most existing literature where Bitcoin has been pronounced most volatile among conventional and cryptocurrencies (see for example (Baur and Dimpfl, 2021, Diniz et al., 2022, Jiang et al., 2022, Zhang and Mani, 2021). Our findings may not be significant, but we stand against most of the existing findings arguing that Ethereum is more volatile than Bitcoin, which is evident through their rocky spikes as opposed to Bitcoin's spikes. Similarly, concerning extreme global events, we observe that Ethereum presents aggressive movements, which are persistent through the presence of a substantial margin between Ethereum's volatility and the highest among the rest (Nikkei 225 index), which differs almost two-fold (Aydoğan et al., 2022, Beneki et al., 2019). Similarly, the CVI index, we observe their high volatility among others. However, our observation states Ethereum and CVI moving in the same pattern as evident from their volatility connectedness.

Figure 7.  Dynamic volatility connectedness among indices.

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With respect to commodity indices, we observe similarities with cryptocurrencies. Even though commodities and gold, in particular, are considered one of the most stable among others, disregarding the fact, our observation shows that gold has been the leader in volatility compared to stock indices. One possible explanation for this could be that gold's price may be linked to global and regional economic conditions. That is, with the rise (fall) in global and regional economic uncertainties and crises, gold price tends to move upwards (downwards), and other indices follow (mostly inversely) and react accordingly, which is evident at times of the Covid pandemic where we find sharp spikes indicating sharp fall in conventional stock indices and flight to safety to gold (Akhtaruzzaman et al., 2021, Junttila et al., 2018, Kamal et al., 2022, Kanjilal and Ghosh, 2017, Wang et al., 2016a) which increased the daily return spreads. Thus, this may constitute the growth in the volatility of Gold as for the past few years, several significant events associated with uncertainties took place in global and financial markets, which has been discussed in our dynamic return connectedness section above. Similarly, for WTI, even though replicating cryptocurrencies and gold by leading in volatilities over other indices, we observed a stable movement until the pandemic struck, showing the worst period in the oil industry for decades (Iglesias and Rivera-Alonso, 2022), thus magnifying the daily return spread between oil and other indices. Surprisingly, during the recent oil crisis, even though a little wider margin was observed over February and March 2022 between oil and stock indices, they were not as significant as those during the Covid periods.

Similar to the return analysis, we further analyzed our volatility series with wavelet coherence to understand the volatility clustering over different investment horizons and to understand any presence of volatility spillover. The wavelet coherence of volatility is documented in Figures 8–12.

Figure 8.  Volatility spillover between Bitcoin and stock indices.

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Figure 9.  Volatility spillover between Ethereum and stock indices.

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Figure 10.  Volatility spillover between CVI and stock indices.

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Figure 11.  Volatility spillover between Gold and stock indices.

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Figure 12.  Volatility spillover between WTI and stock indices.

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3.2.4.   Volatility spillover

Figures 8–12 display the wavelet coherence among volatilities of the respective indices. Overall, we note similarities among the wavelet coherence representations where a substantial amount of volatility clustering is spotted between 2019 to 2021 when Covid-19 was present. For the volatility coherence in relation to cryptocurrencies in Figure 8–10, we note similarities among both the cryptocurrencies and the CVI index where, in most of the observed cases, we find that stock indices are leading against cryptocurrencies indicating volatility spillover from stock indices to cryptocurrencies. Even though 2018 was the year of great crash for cryptocurrency and Bitcoin in particular, we observe only mild (~0.4–0.6) volatility clustering among indices with FTSE Indonesia, being different only where the least volatility presence is observed. Speaking of the pandemic period, despite the presence of the highest volatility clustering, which is limited only to investment horizons for 32 days and beyond, relatively lower volatility is present for lower frequencies, thus making low-frequency investment horizons a safer investment horizon at times of global crises (Polat and Kabakçı Günay, 2021, Umar and Gubareva, 2020). The clustering over longer horizons in 2019 is linked to the global equity market's boom following a slowdown in 2018, and the volatility is a product of the boosted equity markets where equity indices are leading. However, considering the global tension amidst the Russian-Ukraine war, we fail to observe significant volatility clustering among indices except FTSE Malaysia and the S&P 500. The common interpretation is through their linkage to oil markets. That is, even though the USA is one of the leading oil importers, it also exports oil, and the energy price jumps following the start of the war may have resulted in rippling effects from oil markets to the equity and cryptocurrency markets of both the economies (Babar et al., 2024, Guru et al., 2023). The rise in oil price resulted in a global electricity price hike, making cryptocurrency mining costly, leading to a price appreciation, and oil price jump pushed the cost of living upwards, resulting in heightened uncertainty, making financial markets more aggressive. Another possible explanation for this volatility clustering (only for the USA) is through their geopolitical risk channel. With the start of the Russian-Ukraine war, a rise in geopolitical tension among the USA and Russia, and other NATO nations may also have increased the volatility in the US equity markets, contributing to the volatility clustering among cryptocurrencies and developed nation's equity indices (Agyei, 2023, Babar et al., 2024).

Similar to cryptocurrencies, when commodities are considered in Figure 11 and 12, sizeable islands with red plotting are observed, indicating towards presence of volatility clustering. Isolating Nifty, the rest of the pairs display similar outcomes when paired with gold, while for pairs with oil, all six indices document the same story.

With gold (Figure 11), pairwise volatility clustering started to clot starting Mid-2018 when global stock markets began to receive a heavy shock with the trade war, followed by tariff imposition, causing S&P 500 and Nikkei 225 to lose nearly 20% each, FTSE 100 15%, and FTSE Malaysia 10% over the next quarter, but Nifty benefited the most due to their competitiveness with the Chinese market. Our coherence analysis on volatility among gold and stock indices for pre-pandemic periods shows stock indices having a volatility spillover effect over gold. Similarly, during the pandemic also, we noticed the stock market's spillover affecting gold's volatility, which is valid only for longer horizons. For horizons between 16–32 days, the volatility spillover effect from gold to stock indices are noted; however, no presence of volatility clustering spillover is observed for a shorter version of investment horizons. Therefore, our results replicate empirical findings on gold and the stock market's nexus that stock markets can be a good signaling agent for volatility trends in gold markets. That is, at times of falling (rising) stock markets, the volatility spillover from stock to gold is persistent through aggressive upwards (downwards) price movement (Mensi et al., 2022, Zhang et al., 2021).

Unlike gold, the volatility plotting for oil started to become visible from early 2018 (Figure 12), where in all cases, volatility from WTI leading stock indices indicated the presence of volatility spillover from WTI to stock markets over the long run (64 days and beyond). However, similar to gold-stock volatility, no volatility clustering and volatility spillover are observed for short- and medium-term investment horizons. This empirical finding indicates for close observation of the oil market for beneficial and strategic position in stock markets (Jiang and Yoon, 2020, Liu et al., 2023, Salisu et al., 2020, Mensi et al., 2023).

3.2.5.   Portfolio Analysis – Robustness and weight

In line with Baur and Lucey's (2010) classification, assets can function as diversifiers, hedges, or safe havens. A diversifier maintains a positive but imperfect correlation with another asset, while a hedge remains uncorrelated or negatively correlated on average. A safe-haven asset, however, displays negative or zero correlation during periods of market distress. Applying Wavelet Quantile Correlation (WQC), an asset qualifies as a safe haven if its correlation turns negative in lower quantiles (Kumar & Padakandla, 2022; Patel et al., 2024). Moreover, hedge assets exhibit negative correlations, primarily in median quantiles, signifying their ability to mitigate risk over regular market conditions.

The results presented in Figure 13 highlight the wavelet quantile correlation between Bitcoin (BTC) and various financial assets, revealing a heterogeneous correlation structure across time scales. In the short term, BTC exhibits a negative correlation with FTSE 100, FTSE MY, NIKKEI 225, and NIFTY in the lower quantiles, suggesting safe-haven properties during periods of market stress. However, FTSE INDO and S&P 500 display a positive correlation with BTC, indicating limited hedging potential and weak diversification benefits. This trend persists in the medium term, reinforcing BTC's inability to act as a hedge for these assets. Additionally, a consistent positive correlation across all quantiles in the short term suggests that BTC does not offer meaningful hedging or diversification benefits for certain assets. This can be attributed to BTC's speculative nature and high volatility, which make it more suitable for short- and medium-term portfolio adjustments than a reliable long-term hedge.

Figure 13.  Wavelet quantile correlation between Bitcoin (BTC) and financial assets.

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Figure 14.  Wavelet correlation results between Cryptocurrency Volatility Index (CVI) and other financial assets.

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The wavelet correlation analysis between the Cryptocurrency Volatility Index (CVI) and other financial assets, as shown in Figure 2, reveals a heterogeneous correlation structure across time scales. In the short term, only FTSE INDO exhibits a negative correlation in the lower quantile, indicating that CVI may serve as a safe haven for this particular asset during market distress. However, the remaining assets display a consistent positive correlation with CVI in the short term, suggesting limited hedging effectiveness and weak diversification opportunities. This implies that during periods of heightened volatility, CVI moves in tandem with most assets rather than acting as a protective instrument. On medium scales, the correlation patterns remain largely unchanged, reinforcing the notion that CVI does not provide significant hedging or diversification benefits for most assets. The persistence of a strong positive correlation across all quantiles in the short term further suggests that CVI behaves more like a risk-sensitive asset than a defensive one. This finding aligns with the nature of volatility indices, which tend to be highly responsive to market sentiment and fluctuations, thereby making them less suitable as hedging tools against traditional financial assets.

Figure 15.  Wavelet correlation results between Ethereum (ETH) and financial assets.

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The wavelet correlation analysis in Figure 3 illustrates the relationship between Ethereum (ETH) and financial assets, revealing a heterogeneous correlation structure. In the short term, FTSE INDO demonstrates a negative correlation in the lower quantile, indicating ETH's potential as a safe haven for this asset during periods of market distress. However, the rest of the assets show a positive correlation with ETH in the short term, implying minimal hedging capabilities and limited diversification opportunities. This suggests that, rather than providing stability, ETH tends to move in the same direction as these assets, reducing its effectiveness as a risk management tool. On medium scales, the correlation patterns remain unchanged, further reinforcing the notion that ETH does not serve as a hedge or diversification asset for most financial markets. The consistent positive correlation across all quantiles in the short term indicates that ETH does not offer protective benefits, as it tends to co-move with traditional assets rather than counteract their fluctuations. This outcome can be attributed to ETH's speculative nature and strong integration with broader financial markets. As Ethereum has grown in popularity and adoption, it has exhibited increased sensitivity to market trends and macroeconomic factors, leading to higher co-movement with equities and other asset classes.

Figure 16 presents the wavelet correlation results for gold, highlighting its relationship with various financial assets. Gold exhibits a negative correlation with most assets, reinforcing its traditional role as a hedge and safe haven. However, exceptions are observed with the S&P 500 and FTSE 100, which display a positive correlation with gold. This result can be explained by the tendency of these indices to reflect broader economic conditions, where gold, at times, moves in tandem with equities due to investor sentiment shifts or inflation hedging behavior. The negative correlation across multiple assets, especially in lower quantiles during periods of market stress, supports gold's reputation as a protective asset during financial downturns. This characteristic makes gold particularly valuable for investors seeking stability and risk mitigation during global crises. The persistence of this negative correlation in both short- and medium-term scales suggests that gold maintains its hedging effectiveness over different time horizons. However, the positive correlation with S&P 500 and FTSE 100 indicates that gold's hedging ability is not universal and can vary based on macroeconomic conditions, monetary policy changes, and inflation expectations. During periods of economic expansion or rising equity markets, gold may attract investment demand driven by inflation concerns, reducing its inverse relationship with stocks. These findings emphasize that while gold is a reliable hedge and weak safe haven, its effectiveness can be asset-dependent and influenced by market conditions.

Figure 16.  Wavelet correlation results for gold.

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Figure 17 presents the wavelet correlation results for WTI oil, revealing its dynamic relationship with various financial assets across different time horizons. In the short and medium term, WTI oil exhibits a negative correlation with most assets, suggesting its potential role as a hedge during periods of market turbulence. This negative correlation implies that oil prices tend to move inversely to other financial assets, making it a useful instrument for diversification and risk management in shorter investment horizons. Such behavior can be attributed to economic uncertainty, where investors shift capital away from equities and into commodities like oil, particularly when geopolitical risks or supply-side shocks impact energy markets. In contrast, the long-term correlation between WTI oil and other assets turns positive, indicating that over extended periods, oil prices tend to move in tandem with broader financial markets. This shift can be explained by oil's fundamental connection to economic growth, as higher demand for energy typically coincides with expanding economies and rising stock markets. Additionally, long-term macroeconomic factors, such as inflation, monetary policy, and global trade dynamics, contribute to this alignment between oil and other asset classes. The findings suggest that while WTI oil can serve as a hedge in the short to medium term, its effectiveness diminishes over longer periods when its correlation with equities strengthens. This highlights the importance of investment horizon considerations when using oil as a diversification tool. Investors may benefit from oil's hedging properties during market shocks but should be aware that its long-term performance is more closely linked to economic cycles and global demand trends.

Figure 17.  Wavelet correlation results for WTI oil.

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The hedging ratios for each bivariate portfolio are shown in Table 2. Among all the portfolios, we report some significant ones. The Gold/FTSE Indo holds the highest portfolio weight of 0.65. This indicates to an investor that by investing $\$$1.00 in this portfolio, $\$$0.65 will go to Gold and $\$$0.35 will go to FTSE Indo. The higher weight suggests that this portfolio will contribute more to portfolio performance when compared to other portfolios. The Bitcoin and FTSE Indo, BTC/FTSE Indo has a weight of 0.07, meaning $\$$1 invested in this portfolio will spread by $\$$0.07 in Bitcoin and $\$$ 0.93 in FTSE Indo. Additionally, the assigned weight found to be.04 and 0.96 in the case of Ethereum/FTSE Indo paring. If an investor invests $\$$1.00 in this portfolio then approximately $\$$0.04 will be invested in Ethereum, and $\$$0.96 will be invested in FTSE Indo.

Table 2.  Bilateral portfolio results.

	Weight	Hedging Effectiveness	Sharpe Ratio	Hedge Ratio
Gold/BTC	0.97	0.02	0.48	0.01
Gold/ETH	0.98	0.01	0.46	0
Gold/WTI	0.88	0.1	0.34	0.01
Gold/NIFTY	0.53	0.41	0.84	0.01
Gold/FTSE INDO	0.65	0.31	0.37	0
Gold/NIKKIE225	0.62	0.38	0.56	−0.05
Gold/FTSE MY	0.36	0.59	0.09	0.04
Gold/FTSE100	0.51	0.41	0.32	0
Gold/S&P500	0.52	0.39	0.79	−0.03
BTC/Gold	0.03	0.97	0.48	0.23
BTC/ETH	0.67	0.24	1.17	0.07
BTC/WTI	0.24	0.76	0.2	0.07
BTC/NIFTY	0.04	0.95	0.79	0.33
BTC/FTSE INDO	0.07	0.92	0.29	0.19
BTC/NIKKIE225	0.05	0.94	0.52	0.27
BTC/FTSE MY	0.02	0.98	−0.04	0.35
BTC/FTSE100	0.02	0.95	0.19	0.66
BTC/S&P500	0.03	0.92	0.39	0.93
ETH/Gold	0.02	0.98	0.46	0.18
ETH/BTC	0.33	0.62	1.17	0.14
ETH/WTI	0.16	0.86	0.09	−0.01
ETH/NIFTY	0.01	0.97	0.66	0.86
ETH/FTSE INDO	0.04	0.96	0.28	0.16
ETH/NIKKIE225	0.02	0.97	0.48	0.6
ETH/FTSE MY	0.01	0.99	−0.13	0.87
ETH/FTSE100	0.01	0.98	0.11	0.97
ETH/S&P500	0.02	0.96	0.26	0.56
WTI/Gold	0.12	0.95	0.34	0.06
WTI/BTC	0.76	0.64	0.2	0.02
WTI/ETH	0.84	0.57	0.09	0
WTI/NIFTY	0.14	0.93	0.49	0
WTI/FTSE INDO	0.21	0.89	0.05	0.08
WTI/NIKKIE225	0.18	0.92	0.35	0.12
WTI/FTSE MY	0.07	0.97	−0.16	0.13
WTI/FTSE100	0.1	0.93	−0.07	0.29
WTI/S&P500	0.12	0.9	0.02	0.38

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The hedging ratios for each bivariate portfolio are also shown in Table 2- With a hedge ratio of 0.97, The ETH/FTSE100 portfolio has the highest. This hedge ratio indicates that if an investor takes a $\$$1 long position in Ethereum, then they can effectively hedge their position by shorting FTSE100 for $\$$0.97. This hedge ratio implies that these two assets have a strong negative correlation in the short term. The situation implies that changes in the value of FTSE100 is offset by opposite movements in ETH. On the other hand, Gold/FTSE100 has the lowest hedge, which is 0. This suggests that Gold and FTSE100 have no correlations.

4.   Conclusions

The global financial market has been insecure; hence, a safe investment zone has been indispensable. Whether cryptocurrencies can fulfill investors' needs by safeguarding them during times of crisis has been debated since their introduction. With current market conditions and growing uncertainty, we attempt to identify differences with earlier times and to seek potential evidence favoring cryptocurrency investments. We used one of the under-utilized dynamic methods in financial literature (wavelet coherence) besides DCC-GARCH, with a dataset from July 27, 2016 to December 30, 2022 to investigate possible safe haven instruments for emerging and developed stock markets. Additionally, we investigate the volatility of the respective indices to identify their directional spillovers.

We argue Ethereum's capability to act as a safe haven for investors from both emerging and developed markets at a time of sudden shock (or pandemic), while Bitcoin offers limited safeguarding (only for FTSE Indonesia over the shortest horizon). Ethereum's superiority lies in its ability to support smart contracts, and decentralized applications (dApps) may make it more resilient during crises, as it is seen as a platform for innovation and long-term value creation. Also, Ethereum is often perceived as a more stable and technologically advanced cryptocurrency compared to Bitcoin, which may contribute to its stronger safe-haven properties. Additionally, the increasing institutional adoption of Ethereum, particularly in the decentralized finance (DeFi) space, may also play a role in its performance during crises.

However, with recent growing geopolitical tension, we note both cryptocurrencies holding high positive connectedness with stock indices due to energy price jumps; thus, our evidence suggests not to hold cryptocurrencies and stocks at times of rising oil price-related uncertainties or vice versa. We also argue that cryptocurrencies lead all stock indices for most of the observed periods, connotating the potential use of cryptocurrencies as signaling agents for the stock market movements; thus, policy makers should also pay adequate attention in relation to cryptocurrencies. For gold, we show evidence of high positive coherence among stock and gold over a long period where stock indices were leading during the recent pandemic whereas a weak coherence is observed during the geopolitical tensions amidst the Russian-Ukraine war and energy supply cut. Hence, we argue gold as a hedge during global crises while a hedge and weak safe haven against geopolitical tension.

As of today, oil dominates as the global economic factor of production as well as economic drivers; thus, oil plays a key role in influencing financial markets. In line with most empirical findings, we find a higher order of coherency among stock indices from both emerging and developed nations and the crude oil index we used. Relatively lower coherency is noted over shorter horizons, making a shorter ideal holding period for oil-stock investment. However, for longer versions, we argue returns from holding oil and stock may bring beneficial financial positions but may vanish through inflation due to the rising cost of living by rising oil impacts, which may be a possible direction for further studies.

Considering volatility connectedness, our DCC GARCH findings reveal surprising and distinctive facts from most available literature. Based on our evidence, we argue, in general, that Ethereum is more volatile than Bitcoin, which is evident through their rocky spikes as opposed to Bitcoin's spikes, which are consistent even throughout extreme global events. We observe that Ethereum has aggressive movements that are persistent through the presence of a substantial margin between Ethereum's volatility and other's volatility, which differs almost two-fold. Moreover, we find Ethereum and CVI moving in the same pattern as evident from their volatility connectedness. Similarly, when analyzed for commodity markets, we find volatility of both gold and oil indices are the highest among others.

Concerning volatility spillover, we found that for almost all the periods and horizons assessed, stock markets are net volatility transmitters while cryptocurrency markets are net volatility receivers. In particular, the highest volatility clustering was noticed only during Covid-19 for longer horizons and not for shorter versions of investment horizons. Surprisingly, we fail to observe noteworthy clustering. However, among all stock indices, we found relatively less volatility clustering among cryptocurrencies and the FTSE Indonesian index, while most Developed market stock indices had a relative higher volatility clustering and spillover impact with cryptocurrency.

For commodity markets, the pre-pandemic period, and during-pandemic period, we show that stock indices have a volatility spillover effect over gold only for longer horizons; however, for investment horizons ranging from 16–32 days, stock markets are net volatility receivers. Hence, we claim the stock market's movement as a signaling agent for investors to consider gold as an investment protection avenue. For oil, a consistent volatility spillover running from oil to the stock market has been observed; thus, close monitoring of the oil price dynamic may be abstrusely beneficial for stock market investors to secure their investment, especially at times of market turmoil.

The study and findings, thus, suggest that, due to the enlarged volatility, the volatility connectedness, and the volatility spillover between the cryptocurrencies, the equity markets, and the commodity markets, investors should become additionally cautious when looking into investment portfolios and investment horizons during crises such as the Chinese market crisis, the US-China trade war, the COVID-19 pandemic, and the Russia-Ukraine war.

5.   Novelty and contribution

The novelty of this research lies in the inclusion of Ethereum, CVI, and geopolitical tension. Unlike many researchers who focus primarily on Bitcoin, we include Ethereum, the second-largest cryptocurrency by market capitalization, and compare its hedging properties with Bitcoin and traditional assets like gold. We introduce the Crypto Currency Volatility Index (CVI) as a new variable, which has not been extensively analyzed in prior research. This provides a fresh perspective on the volatility dynamics of cryptocurrencies. We examine the impact of recent geopolitical events, such as the Russia-Ukraine war, on the hedging properties of cryptocurrencies, which has not been thoroughly explored in other studies.

This study can help investors, portfolio managers, and policymakers in making hedge decisions. During times of market turbulence—like geopolitical tensions or pandemics—investors might consider increasing their portfolio allocation to Ethereum, as it has shown stronger safe-haven properties compared to Bitcoin. Bitcoin, on the other hand, could be used more for limited risk diversification than as a strong hedge. Portfolio managers could use Ethereum as a short-term hedge during crises, while Bitcoin might be better suited for diversification in less volatile market conditions. Policymakers should keep an eye on the growing integration of cryptocurrencies with traditional financial markets. Our findings suggest that cryptocurrencies, especially Ethereum, are becoming more correlated with stock markets during crises. This could have significant implications for financial stability and regulatory frameworks.

Author contributions

Rubaiyat Ahsan Bhuiyan conceived and designed the study. Rubaiyat Ahsan Bhuiyan and Kazi Md Tarique conducted the empirical analysis. Tanusree Chakravarty Mukherjee reviewed the literature and drafted the manuscript. Visualizations were prepared by Rubaiyat Ahsan Bhuiyan and Changyong Zhang. All authors participated in the review, editing, and approval of the final version of the manuscript.

Use of AI tools declaration

The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.

Conflict of interest

The authors declare no conflict of interest in this paper.